Published in |
Journal of Gökova Geometry Topology, Volume 11 (2017) |
Title |
Bilinear-form invariants of Lefschetz fibrations over the 2-sphere
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Author |
Takefumi Nosaka
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Abstract |
We introduce invariants of, in general, Hurwitz equivalence classes with respect to arbitrary group G.
The invariants are constructed from any right G-module M and any G-invariant bilinear function on M, and are of bilinear forms.
For instance, when G is the mapping class group, \(\mathcal M_g\), of the closed surface \(\Sigma_g\) of genus g, we get an invariant of 4-dimensional Lefschetz fibrations over the 2-sphere.
Moreover, the construction is applicable for the quantum representations of \(\mathcal M_g\)
derived from Chern-Simons field theory.
We also see that our invariant is unstable with respect to fiber sum of Lefschetz fibrations.
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Keywords |
Bilinear form, 4-dimensional Lefschetz fibration, mapping class group, monodromy, link.
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Pages | 32-55 |
Download |
PDF |
Submitted: | May 16, 2017 |
Accepted: | Jan 23, 2018 |
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